A novel method of modeling multiple frequency dielectrophoresis (MFDEP) is introduced based on the concept of an effective Clausius-Mossotti factor, CMeff, for a particle that is exposed to electrical fields of different frequencies, coming either from one or multiple pairs of electrodes. This analysis clearly illustrates how adding frequencies adds control parameters, up to two additional parameters per frequency. As a result, MFDEP can be used for a wide variety of applications, including separating particles with very similar Clausius-Mossotti spectra, trapping multiple groups of cells simultaneously, and cancelling unwanted dielectrophoretic traps. Illustrating the modeling approach, we determine the CMeffs for live and dead yeast cells, and then predict their equilibrium distribution on a three-electrode configuration, with two electrodes at different frequencies and the third electrode at ground. This prediction is validated experimentally, using MFDEP to selectively attract live cells to one location and dead cells to another, trapping both. These results demonstrate that the use of multiple frequencies for the manipulation of particles can enhance the performance of dielectrophoretic devices, not only for sorting, but also for such applications as patterning cells in close proximity for the formation of cell consortia.